To find first-order linear differential equations solution, we have to derive the general form or representation of the solution.
With the help of the steps shown below, we can learn how to solve the first-order differential equation.
1. Reorder the terms in the given equation so that they have the form [tex]$\frac{dy}{dx}+Py=Q[/tex] where P and Q are constants or functions of the independent variable x only.
2. Integrate P (obtained in step 1) with respect to x and then put this integral as a power of e to determine the integrating factor.
[tex]$e^{\int P d x}[/tex] = IF
3. The linear first-order differential equation's two sides should be multiplied by the IF.
4. The L.H.S of the equation is always a derivative of [tex]$y \times M(x)$[/tex] i.e. L.H.S [tex]$= \frac{d(y \times I . F)}{dx}[/tex]
[tex]$d(y \times I . F) d x=Q \times I . F$[/tex]
5. In order to arrive at the solution, we simply integrate both sides with respect to x in the last step.
Therefore [tex]y \times I . F=\int Q \times I . F d x+C$,[/tex]
where C is some arbitrary constant
Similarly, we can also solve the other form of linear first-order differential equation [tex]$\frac{dy}{dx}+Py=Q[/tex] using the same steps.
P and Q are y's functions in this manner. We determine the solution, which will be, by using the integrating factor (I.F), which is
[tex]$(x) \times(I . F)=\int Q \times I . F d y+c$[/tex]
Now, to get a better insight into the linear differential equation, let us try solving some questions. where C is some arbitrary constant.
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How do I find the value of two numbers if their sum is 12 and their difference is 4?
Answer:
The value of two numbers if their sum is 12 and their difference is 4 are 8 and 4.
Step-by-step explanation:
I hope this helped
Your friend says, "We will each roll a die. If the highest number out of the two dice is a 5 or a 6, gaberil wins. And if the highest number out of the two dice is a 1, 2, 3, or 4, then justen win. Whoever wins the most out of ten tries, wins the taco. "
what is the that justen wins
The probability that Justen wins is 4/9.
Determine the probabilityThe probability that Justen wins is determined by the likelihood that the highest number rolled on the two dice is a 1, 2, 3, or 4. To find this probability, we can first calculate the probability that the highest number rolled is a 5 or 6, which is what would cause Gaberil to win.
The probability of rolling a 5 or 6 on one die is 2/6, or 1/3. The probability of rolling a 5 or 6 on both dice is (1/3) * (1/3) = 1/9.
However, we also need to account for the possibility that one die rolls a 5 or 6 and the other does not.
This can happen in two ways: either the first die rolls a 5 or 6 and the second does not, or the first die does not roll a 5 or 6 and the second does.
The probability of each of these scenarios is (1/3) * (2/3) = 2/9.
So the total probability of Gaberil winning is 1/9 + 2/9 + 2/9 = 5/9.
Since there are only two possible outcomes (either Gaberil wins or Justen wins), the probability of Justen winning is 1 - the probability of Gaberil winning. So the probability of Justen winning is 1 - 5/9 = 4/9.
Therefore, the probability that Justen wins is 4/9.
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PLEASE HELP NEED SOON!!!!!!!!!!!! WILL GIVE BRAINLIEST TO BEST ANSWER!
do the following calculations
1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9 2. 11 > -2 Add 3 to both sides, then add 3, then add (-4) 3. -2 = -2 Subtract 6 from both sides, then 8, and then 2 4. -4 < 8 Divide both sides by -4, then by -2 5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
The expressions are evaluated below
How to evaluate the expressionsExpression 1: 4 < 7
Multiplying both sides by 3, 2, 4, and 9 respectively:
3 * 2 * 4 * 9 * (4 < 7)
864 < 1515
Expression 2: 11 > -2
Adding 3 to both sides, then adding 3, then adding (-4) respectively:
3 + 3 - 4 + (11 > -2)
13 > 0
Expression 3: -2 = -2
Subtracting 6 from both sides, then adding 8, then adding 2 respectively:
-2 + 6 + 8 + 2 = -2 + 6 + 8 + 2
14 = 14
Expression 4: -4 < 8
Dividing both sides by -4, then by -2 respectively:
-4/(-4 * -2) < 8/(-4 * -2)
-1/2 < 1
The operations performed on the inequalities in each question did not affect the inequality sig.
The truth of the inequality was also not affected by the operations in all cases.
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You bought a pair of shoes for $36. If their original price was $84, what percent of the original price did you pay?
Set up a proportion to help you solve this problem
Solve the proportion.
Answer:
43%
Step-by-step explanation:
Something to do with msth not sure js smart wnough to guess it but trust me thats the answer
What is the intermediate step in the form (x+a)2 = b as a result of completing the square for the following x^2=16x+8
The intermediate step in the form (x+a)2 = b is (x - 8)^2 = 72
How to determine the intermediate stepFrom the question, we have the following parameters that can be used in our computation:
x^2 = 16x + 8
Rewrite as
x^2 - 16x = 8
Take the coefficient of x
k = 16
Divide by 2
= 8
Square the quotient
= 64
So, we add 64 to both sides of the equation
So, we have
x^2 - 16x + 64 = 8 + 64
Express as squares and evaluate
(x - 8)^2 = 72
Hence, the intermediate step is (x - 8)^2 = 72
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Which picture corresponds to the correct graph of the points A = (-2, -3), B = (4, 1)., C = (-2, 3), and D = (0, -1)?
The second graph given in the figure attached below is a correct representation of the given points.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, few points on cartesian plane A = (-2, -3), B = (4, 1)., C = (-2, 3), and D = (0, -1)
The xy pairs of a cartesian point are written in parenthesis as follows: (x, y).
To graph a point, first determine where it lies on the x-axis, then determine where it lies on the y-axis, and lastly plot the intersection of these two axes.
Due to its location at the intersection of the x- and y-axes, the origin of the graph, also known as the point (0, 0), is the center of the diagram.
For point A(-2, -3)
Find the negative 2 on the x-axis and the negative 3 on the y-axis, for instance, to draw the point (-2, -3).
The same will go for the remaining three points.
Therefore, The second graph given in the figure attached below is a correct representation of the given points.
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If it takes 4 people 6 hours to build a wall how long will it take 3 people to complete the same task
how much usd for 800 yen?
Since, 1 JPY = 0.0077 USD in Jan 27, 2023 08:45 UTC
Therefore, based on above information :
800 Japanese Yen 5.93 US Dollar.
The yen is the official currency of Japan. It is the third most traded currency on the foreign exchange market, after the US dollar (USD) and the euro. It is also widely used as the third key currency after the US dollar and the euro.
After World War II, the yen lost much of its pre-war value. To stabilize the Japanese economy, the yen exchange rate was fixed at 360 yen per US dollar under the Bretton Woods system. When this system was abolished in 1971, the yen was devalued and became liquid. After peaking at 271 yen per dollar in 1973, the yen appreciated to 271 yen per dollar due to the oil crisis in 1973, reaching 227 yen per dollar in 1980.
Another option is to do the calculations manually using simple mathematical formulas. However, for this you need to know the current exchange rate. As of this writing, one yen is worth $0.007.
Once you know this information, multiply the amount in JPY by the current exchange rate.
The resulting number shows how much you need to spend on your trip in US dollars.
Manual Currency Conversion Example
Suppose you have 100,000 yen and want to calculate how much money you will need to travel to the United States. Using the current exchange rate, the conversion formula would be
100,000 yen x 0.007 = $700
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Araceli uses 8. 7 pints of blue paint and white paint to paint her bedroom walls. 1/4
of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
Express your answer in fraction and decimal form. Solve on paper. Then check your work on Zearn
The amount of white paint did she use to paint her bedroom walls is 6 21/40 or 6.525 pints.
To find the amount of white paint used, we first need to find the amount of blue paint used. Since 1/4 of the total amount of paint is blue, we can multiply the total amount of paint by its fraction, 1/4, to find the amount of blue paint:
Blue paint = 8.7 pints × 1/4 = 87/40 = 2.175 pints
Now, to find the amount of white paint used, we can subtract the amount of blue paint from the total amount of paint:
White paint = 8.7 pints - 2.175 pints = 261/40 = 6.525 pints
So, Araceli used 6.525 pints of white paint to paint her bedroom walls.
In fraction form, this can be written as 6525/1000 pints, or 6 21/40 pints.
In decimal form, it is simply 6.525 pints.
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a park in the shape of a rectangle 2.5 miles long and 1.25 miles wide if you walk diagonally across the park how many miles will you walk
Answer: You will walk 2.795 miles
Step-by-step explanation:
You can solve this using the Pythagorean theorem which is a^2 + b^2 = c^2
Plug in your numbers so you have 2.5^2 + 1.25^2 = c^2
Simplify that down to 6.25 + 1.5625 = c^2
Add 7.8125 = c^2
Find the square root of each of them. 2.795 = c
I don't know how you want me to round the answer so I just did it to the nearest thousandths.
How much 30000 won to usd ?
The value of 30000 south korean currency is $25.50.
To convert 30000 South Korean Won to US Dollars, we can use the current exchange rate between the two currencies.
1. First, we need to find the current exchange rate between South Korean Won and US Dollars. As of September 9th, 2021, the exchange rate is 0.00085 USD per 1 South Korean Won.
2. Next, we can multiply the amount of South Korean Won we have by the exchange rate to find the equivalent amount in US Dollars.
30000 South Korean Won * 0.00085 USD/South Korean Won = 25.50 USD
3. Therefore, 30000 South Korean Won is equivalent to 25.50 US Dollars.
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what is the answer ?
In the triangle that we have here cos 42 degrees is equal to sin 48
How to solve for the angleThis was simply solved using the calculator
cos 42 = 0.7431
sin 42 = 0.6691
cos 48 = 0.6691
sin 48 = 0.7431
From the above we can see that the value of cos 42 and sin 48 returned the same digits at 0.7431
Hence the value of cos 42 is sin 48 degrees
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growth or decay
0.27
Answer:
The answer to this question is DECAY!
Step-by-step explanation:
this is decay because the decimal is below one if it was above one this would be growth.
good luck!
SOMEONE PLS HELPP FAST
picture below
The graph representing the association will be a negative linear association. Then the correct option is C.
What is the association?The form, direction, confidence, and outliers of an association (relationship) between two quantitative variables can be used to describe it. • A positive association exists when one variable increases as the other dependent variable.
There is no boundary and all the dots are widely dispersed if there is no association. Variational individuals who are part that the dots are close together but not in a straight line.
From the graph, the slope of the best line will be negative.
The graph representing the association will be a negative linear association. Then the correct option is C.
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A highway camera films cars daily as they pass by. Over a
two-month period, the camera shows that 16% of the cars that
pass by are silver. If 50 cars are selected at random on one
day, which is the expected number of cars which are a color
other than silver?
A
B
C
D
8 cars
16 cars
34 cars
42 cars
The expected number of cars that are a color other than silver is 42 cars.
Option D is the correct answer.
What is a percentage?The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying it by 100.
The percentage change is also calculated using the same method.
In percentage change, we find the difference between the values given.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
If 16% of the cars passing by are silver, then the percentage of cars that are not silver.
= 100% - 16%
= 84%.
If 50 cars are selected at random on one day, the expected number of cars that are a color other than silver is equal to the total number of cars (50) multiplied by the percentage of cars that are not silver (84%).
= 50 x 84%
= 50 x 0.84
= 42 cars
Therefore,
The expected number of cars that are a color other than silver is 42 cars.
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Keith's bookshelf has 5 shelves. If he has 262 books, estimate the number books he can put on each shelf by rounding the larger number to the neare hundred.
Answer:
52.40
Step-by-step explanation:
Given that,
Keith's bookshelf has 5 shelves.
He has 262 books.
To find the number of books he can put on each shelf.
[tex]required \\ number = \frac{Total Books}{Total Shelves}\\\\= \frac{262}{5} = 52.40[/tex]
Hence 52.40 is the right answer.
Answer:
you in BBC FDA's in BBC FDA's in just had not had not had not had on under end
Step-by-step explanation:
no exception
Find three consecutive even integers such that the sum of the three integers is 90
Unknowns: Let x=first even integer
____= second consecutive even integer
____= third consecutive even integer
Equation:
Solve:
Answer: 28, 30, 32
Step-by-step explanation: The first integer is 28, the second is 30, and the third is 32. The difference from the first integer and the last integer should be 4. x is the first integer, so the equation is:
x+x+2+x+4=90
The first integer plus the second integer(x+2) plus the third integer(x+4) equals 90. Now solve.
x+x+2+x+4=90
3x+6=90
-6 -6
3x=84
/3 /3
x=28
So the first integer is 28, second is 30, third is 32.
Hope this helps!
What is binomial distribution table ?
Answer:
Step-by-step explanation:
A binomial distribution table is a table that lists the probabilities of obtaining a specific number of success outcomes in a fixed number of independent trials, given a constant probability of success in each trial. The binomial distribution is a discrete probability distribution that describes the number of success outcomes in a fixed number of independent trials with a binary outcome (success or failure).
The table lists the probabilities of obtaining k successes in n trials, where k is a non-negative integer and n is a positive integer. The probabilities are calculated using the binomial formula, which is given by:
P(k successes in n trials) = (n choose k) * p^k * (1 - p)^(n-k)
where (n choose k) is the number of ways to choose k success outcomes from n trials, p is the probability of success in each trial, and (1 - p) is the probability of failure in each trial.
Binomial distribution tables are useful for solving problems related to counting and probability, especially in situations where the number of trials is fixed and the probability of success is constant. They can also be used for hypothesis testing, calculating confidence intervals, and estimating population proportions in statistical applications.
help pls
1. Use the relationship PV = nRT to find the number of moles in an amount of gas when the
temperature is 299 K, the pressure is 3 atmospheres, and the volume is 5 liters
(R = 0.0821).
The number of moles is given by the equation n = 0.611 moles
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
PV = nRT be equation (1)
Divide by RT on both sides of the equation , we get
n = PV / RT
Now , when temperature T = 299 K
The value of pressure P = 3 atm
The value of volume V = 5 Liters
The universal gas constant R = 0.0821
Substituting the values in the equation , we get
n = ( 3 x 5 ) / ( 0.0821 x 299 )
On simplifying the equation , we get
n = 15 / 24.5479
n = 0.611 moles
Therefore , the number of moles is 0.611 moles
Hence , the equation is n = 0.611 moles
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Is-39 a solution for the
equation below?
YES or
NO
P/13=3
Answer:
No
Step-by-step explanation:
[tex]\frac{p}{13}[/tex] = 3 ( multiply both sides by 13 to clear the fraction )
p = 13 × 3 = 39
then p = 39 is the solution not p = - 39
[tex] \frac{p}{13} = 3[/tex]
[tex]p = 13 \times 3[/tex]
[tex] = 39[/tex]
Let's solve it first by Method 2 (Systematic Method) :-[tex] \frac{p}{13} = 3[/tex]
[tex] \frac{p}{13} \times 3 = 3 \times 13[/tex]
If we cancel 13 from LHS and RHS both sides[tex] \frac{p}{39} = 3[/tex]
[tex]p = 13 \times 3 \\ = 39[/tex]
[tex]\textbf{\textcolor{red}{Thank you!}}[/tex]
Two water balloons were launched into the air at different moments and collided. The water balloons were modeled by the quadratic functions: y = −7x2 + 26x + 3 and y = −6x2 + 23x + 5, where y represents the height in meters and x represents the time in seconds after the launch. What is the time, in seconds, that the balloons collided at the highest point? 2.0 seconds 2.25 seconds 2.5 seconds 2.75 seconds
The time it takes is 2 seconds
What is the time the balloons collided at the highest point?
To find the time that the balloons collided at the highest point, we need to find the vertex of the resulting quadratic function.
First, we can set the two functions equal to each other, since they represent the height of the two balloons at any given time:
-7x^2 + 26x + 3 = -6x^2 + 23x + 5
Simplifying and rearranging terms, we get:
-x^2 + 3x + 2 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -1, b = 3, and c = 2.
Plugging in these values, we get:
x = (-3 ± sqrt(3^2 - 4(-1)(2))) / 2(-1)
x = (-3 ± sqrt(1)) / (-2)
Simplifying further, we get:
x = (-3 ± 1) / (-2)
So, x can be either 1 or 2. However, we're only interested in the positive value for x since time cannot be negative.
Therefore, the time that the balloons collided at the highest point is:
x = 2 second
So, the correct answer is: 2.0 seconds
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Melanie’s bedroom walls are 45% painted.The area of her walls totals 420 square feet.How many square feet of Melanie’s walls still need to be painted?
Melanie’s walls still needs to be painted is 231 square feet.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, Melanie’s bedroom walls are 45% painted.
The area of her walls totals 420 square feet.
The area of wall painted
=45% of 420
= 45/100 ×420
= 0.45×420
= 189 square feet
Remaining area = 420-189
= 231 square feet
Therefore, Melanie’s walls still needs to be painted is 231 square feet.
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What is monomial representations and symmetric presentations?
Answer: A monomial representation is a way to express a polynomial as a product of powers of its variables, where each power is a non-negative integer. For example, the polynomial 2x^3 + 4x^2 - 6x + 8 can be represented as a monomial representation of (2x^3)(x^2)(-6x)(8).
Symmetric polynomials are polynomials that are invariant under permutation of their variables. A symmetric presentation is a way of expressing a symmetric polynomial as a sum of elementary symmetric polynomials, which are defined as the sum of all possible products of variables taken i at a time, where i ranges from 1 to the number of variables. For example, the symmetric polynomial x^3 + y^3 + z^3 can be expressed as a symmetric presentation of x + y + z.
Step-by-step explanation:
-) Doreen Short was
looking over the
repayment schedule for
a loan of $40,000.00 at
9% interest for 4 years
with a monthly payment
of $995.40. The loan is
paid off with payment
30 with a previous
balance of $17,565.74.
The final payment and amount saved based on the given interest are respectively;
a) $17697.5 and $1215.12
b) $12377.80 and $562.40
How to find the simple Interest?The equation for the interest is mathematically expressed as:
I = balance*percentage/12
Therefore:
I = 17565.74 * 0.09/12
I = 131.7
The final payment is; F = I + B
F = 131.7 + 17,565.74
F = 17697.5
Amount saved
A.S = (19 * 995.40) - 17697.5
A.S = 1215.12
b) For the loan is paid off with payment 36 with a loan balance of $12,285. 66
I= balance*percentage/12
Therefore:
I = (12,285.66 * 0.09)/12I92.142
I = 92.142
Final payment
F = I + B
F = 92.142 + 12377.80
F = 12377.80
Amount saved
A.S = (13 * 995.40) - 12377.80
A.S = $562.40
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The complete question is;
Doreen Short was looking over the repayment schedule for a loan of $40,000. 00 at 9% for 4 years with a monthly payment of $995. 40.
Find the final payment and amount saved if :
A. ) The loan is paid off with payment 30 with a previous balance of $17,565. 74
B. ) The loan is paid off with payment 36 with a loan balance of $12,285. 66
Seventy-four students came to the school dance. About 1/9
of the
students bought their tickets ahead of time. Approximately how many
students purchased their tickets ahead of time?
In the figure, angle A measures 41° and angle D measures 32°. What is the measurement of angle E?
A. 88°
B. 90°
C. 99°
D. 100°
Answer:C
Step-by-step explanation:
interior angles of a triangle, when added, = 180
so < A + < B + < C = 180
41 + 90 + < C = 180
131 + < C = 180
< C = 180 - 131
< C = 49
< C + < D + < E = 180.....because when added they form a line
49 + 32 + < E = 180
81 + < E = 180
< E = 180 - 81
< E = 99 <======
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what is v64 + 36 smplified
Answer: D.) 14
Step-by-step explanation:
First, you first calculate the square root of 64 , this gives you 8
Next, you calculate the square root of 36, which gives you 6
Then, since you are asked to add the two, you add 8 + 6 since this is the simplified version of the original equation.
8 + 6 = 14
Therefore, your answer is D.) 14
How do you convert micrometers to centimeters?
Divide the number of micrometers by 10,000 to get the equivalent number of centimeters.
To convert micrometers to centimeters, you need to use the conversion factor between the two units. There are 10,000 micrometers in a centimeter.
Here are the steps to convert micrometers to centimeters:
1. Start with the number of micrometers you want to convert.
2. Divide the number of micrometers by 10,000 to get the equivalent number of centimeters.
3. The result is the number of centimeters equivalent to the given number of micrometers.
For example, if you want to convert 50,000 micrometers to centimeters, you would divide 50,000 by 10,000 to get 5 centimeters.
So, the conversion formula is:
centimeters = micrometers ÷ 10,000
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1. Simplify each of the following.
a^4 divided by a^-2 multiplied by a^7
what a unit of measurement equal to one thousand meters?
A unit of measurement equal to one thousand meters is called a kilometer.
A kilometre is a length measurement in the metric system that is equivalent to 1000 metres because the word "kilo" implies "one thousand". Longer distances, such those between cities or nations or the duration of a marathon, are frequently measured in kilometers. The lower length units of the metric system, such as meter's, centimeters, and millimeters, can be used to measure shorter distances.
A length measurement in the metric system that is 1,760 yards or 5,280 feet long. A metric capacity unit is one thousandth of a liter. a length expressed as a thousandth of a meter in meters. a common measure of time that is equal to 60 seconds and 1/60 of an hour.
Therefore, the kilometer is equal to one thousand meter's.
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